1. Field of the Invention
The present invention relates to continuous-time filters. More specifically, the present invention relates to a continuous-time filter with improved noise performance by down-scaling current flowing into filter capacitors using current mirrors.
2. Description of the Related Art
The design of filters involves handling of a large, complex array of parameters and factors, many of which interact in complex manners. The design task often becomes more complicated when a filter is implemented as an integrated circuit due to the large variation in actual values of passive components even when relative matching of components is good. Several techniques have been proposed to overcome the problem of component value variation in an integrated circuit. Generally these techniques employ some type of electronic adjustment to compensate for variations.
A problem that arises in the design of continuous-time (C-T) integrated filters is the limited capacitor values that are available on an integrated circuit chip because of the area inefficiency of capacitors and resistors. Furthermore, the limited capacitor values have an impact on the noise performance of the filters since the noise generated by passive components in the filter is inversely proportional to the capacitor values.
One example of a filter is a well known first order lowpass filter, illustrated by a reference filter 100 shown in FIG. 1. The reference filter 100 includes an operational amplifier 110 having a noninverting input terminal connected to ground, an inverting input terminal and an output terminal connected to the inverting input terminal through a resistor R and a capacitor C which are connected in parallel. An input voltage is applied to the inverting input terminal via a resistor R. The transfer function of the reference filter is shown in an equation, as follows: ##EQU1##
If the operational amplifier is assumed to be noiseless then the input referred noise density is given in an equation, as follows: ##EQU2## and the total output noise is determined as in an equation, as follows: ##EQU3##
Accordingly, for a sinusoidal input signal with a maximum amplitude of V.sub.max,out applied to the reference filter 100, the dynamic range is given by an equation, as follows: ##EQU4##
The dynamic range is independent of resistor values and depends only on the capacitor value and the maximum output voltage. To minimize noise of the filter, a large capacitor is typically chosen. The choice of a large capacitor value is generally not viable for an integrated C-T filter so that a designer is forced to make a compromise between integrated circuit chip area consumption and noise.
For a first order passive RC filter, the noise voltage is given by kT/C. Referring to the equation describing total output noise, ##EQU5## an active lowpass filter, even though assumed to have a noiseless active component (the operational amplifier), still generates a noise voltage of 2kT/C. The factor of two over the kT/C noise factor is related to filter topology. Other active filter topologies may be designed for low noise operation, but all merely approach but do not better the kT/C limit.
What is needed is a filter circuit and method of filter design that reduces filter noise below an apparently fundamental limit of kT/C for active filters.